24 and 64: All the common factors (divisors) and prime factors of the integer numbers

The common factors (divisors) of two numbers are all the factors (divisors) of the greatest (highest) common factor (divisor), gcf, hcf, gcd.

Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd:

Integer numbers prime factorization:


24 = 23 × 3;


64 = 26;


Multiply all the common prime factors, by the lowest exponents.


Greatest (highest) common factor (divisor):


gcf, hcf, gcd (24; 64) = 23 = 8;

Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd


All the common factors (divisors) and prime factors of the integer numbers 24 and 64?

Find all the factors (divisors) of the GCF (HCF, GCD), 8.

8 = 23

Take each of the GCF's prime factors, and their exponents, if there are, and all their combinations.

Also add 1 to the list of factors (divisors). Any number is divisible by 1.

24 and 64 have 4 common factors (divisors), out of which 1 prime factor, 2:

neither a prime nor a composite = 1
prime factor = 2
22 = 4
23 = 8

Final answer
24 and 64 have 4 common factors (divisors), out of which 1 prime factor, 2:

1; 2; 4 and 8.

common factors (divisors) (24; 6,122) = ?


Calculator: all the (common) factors (divisors) of numbers

Latest calculated (found) factors (divisors)

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Tutoring: factors (divisors), common factors (common divisors), the greatest common factor, GCF (also called the greatest common divisor, GCD, or the highest common factor, HCF)

If "t" is a factor (divisor) of "a" then among the prime factors of "t" will appear only prime factors that also appear on the prime factorization of "a" and the maximum of their exponents (powers, or multiplicities) is at most equal to those involved in the prime factorization of "a".

For example, 12 is a factor (divisor) of 60:

  • 12 = 2 × 2 × 3 = 22 × 3
  • 60 = 2 × 2 × 3 × 5 = 22 × 3 × 5

If "t" is a common factor (divisor) of "a" and "b", then the prime factorization of "t" contains only the common prime factors involved in both the prime factorizations of "a" and "b", by lower or at most by equal powers (exponents, or multiplicities).

For example, 12 is the common factor of 48 and 360. After running both numbers' prime factorizations (factoring them down to prime factors):

  • 12 = 22 × 3;
  • 48 = 24 × 3;
  • 360 = 23 × 32 × 5;
  • Please note that 48 and 360 have more factors (divisors): 2, 3, 4, 6, 8, 12, 24. Among them, 24 is the greatest common factor, GCF (or the greatest common divisor, GCD, or the highest common factor, HCF) of 48 and 360.

The greatest common factor, GCF, is the product of all prime factors involved in both the prime factorizations of "a" and "b", by the lowest powers (multiplicities).

Based on this rule it is calculated the greatest common factor, GCF, (or greatest common divisor GCD, HCF) of several numbers, as shown in the example below:

  • 1,260 = 22 × 32;
  • 3,024 = 24 × 32 × 7;
  • 5,544 = 23 × 32 × 7 × 11;
  • Common prime factors are: 2 - its lowest power (multiplicity) is min.(2; 3; 4) = 2; 3 - its lowest power (multiplicity) is min.(2; 2; 2) = 2;
  • GCF, GCD (1,260; 3,024; 5,544) = 22 × 32 = 252;

If two numbers "a" and "b" have no other common factors (divisors) than 1, gfc, gcd, hcf (a; b) = 1, then the numbers "a" and "b" are called coprime (or relatively prime).

If "a" and "b" are not coprime, then every common factor (divisor) of "a" and "b" is a also a factor (divisor) of the greatest common factor, GCF (greatest common divisor, GCD, highest common factor, HCF) of "a" and "b".


What is a prime number?

What is a composite number?

Prime numbers up to 1,000

Prime numbers up to 10,000

Sieve of Eratosthenes

Euclid's algorithm

Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples